{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "61b10fe5-d1bd-43ee-8efb-d9ce2d579a3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<function chebfit at 0x0000019A93BB82C0>\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAksAAAHFCAYAAADi7703AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAABw1klEQVR4nO3dd1hT598G8DusMIQgIEsRcDEdDAda95511C3iqNtWq122tY4OtbbuOqviFq2jTixuq6iI4BYXKiqIqCxl53n/8EdeI0NAIAncn+vKdZmT55x8n5wTcnvGcyRCCAEiIiIiypWWqgsgIiIiUmcMS0RERET5YFgiIiIiygfDEhEREVE+GJaIiIiI8sGwRERERJQPhiUiIiKifDAsEREREeWDYYmIiIgoHwxLVGCXL1/G0KFD4ejoCH19fVSoUAGenp747bff8OLFC0U7BwcHdOnSpdje9/79+5BIJPj999+LbZkFUdz9+FAODg6QSCSKR4UKFdCwYUOsX7++0Ms6fvw4JBIJjh8/XvyFqkCLFi3QokWLUpvX09NTJdtkacj+vvn7+6vk/X/99Vfs3r07x3RN2WYXL16MGjVqQE9PDxKJBPHx8UVe1pAhQ+Dg4PBB9cycOROurq6Qy+WFmu/WrVvQ09PDxYsXP+j9ywqGJSqQVatWwcvLCyEhIfjqq68QGBiIXbt2oXfv3li+fDmGDx+u6hLLhSZNmiA4OBjBwcHw9/eHRCKBn58fli1bpurSVGrp0qVYunRpqbxXeHg4wsLCAACrV68ulfcsTTY2NggODkbnzp1V8v55hSVPT08EBwfD09Oz9IsqoPDwcHz++edo2bIljh49iuDgYBgbGxd5eVOnTsWuXbuKPP+TJ0/w22+/YebMmdDSKtzPfa1atTBw4EB88cUXRX7/skRH1QWQ+gsODsaYMWPQtm1b7N69G1KpVPFa27ZtMXnyZAQGBqqwwvLD1NQUjRo1Ujxv06YN7O3tMW/ePIwZM0aFlamWq6trqb3XX3/9BQDo3Lkz9u/fjzNnzqBx48al9v5vy8jIgEQigY5O8f0pl0qlStuYujAxMVHLut527do1AMCIESPQoEGDD15e9erVP2j+hQsXwtTUFD179izS/OPHj4e3t7dKt3F1wT1L9F6//vorJBIJVq5cqRSUsunp6aFbt245pgcGBsLT0xMGBgZwdnbGmjVrcrSJiYnBqFGjUKVKFejp6cHR0REzZsxAZmZmjrZyuRy//PILqlatCn19fXh7e+PIkSOK10+dOgWJRIItW7bkmHf9+vWQSCQICQkBANy7dw/9+vWDra0tpFIprKys0Lp1a4SHh5dIPzIyMmBpaQlfX98c88bHx8PAwACTJk3K8dr7mJqawsnJCQ8ePFBM+++//9C6dWsYGxvD0NAQjRs3xv79+/NdzoYNGyCRSBAcHJzjtZkzZ0JXVxdPnjwB8Oawlbu7O0JCQtC0aVMYGhqiWrVqmD17do5d/Q8fPsSgQYNgaWkJqVQKFxcX/PHHH0rtsg/7zJ07F3PmzIGDgwMMDAzQokUL3Lp1CxkZGfj2229ha2sLmUyGHj16IDY2Vul9cjuUNmPGDDRs2BBmZmYwMTGBp6cnVq9ejQ+5d3hqaio2b94MLy8vzJ8/HwBy3R6mT58OiUSCsLAw9OzZEyYmJpDJZBg0aBCePXum1Db7cO+uXbtQp04d6Ovro1q1ali0aJFSu+zDUBs2bMDkyZNRuXJlSKVS3LlzR1FH3bp1oa+vDzMzM/To0QM3btxQzD979mxoaWlh7969SssdMmQIDA0NceXKFQC5H4bL7s/ly5fRu3dvyGQymJmZYdKkScjMzERERAQ6dOgAY2NjODg44LfffsvxuU2ePBn16tVTzOvj44N//vlHqZ1EIsGrV6+wbt06xeHm7PWa12G4PXv2wMfHB4aGhjA2Nkbbtm1zbMfZ9V+7dg39+/eHTCaDlZUVhg0bhoSEhBzrLzfv+3xbtGiBQYMGAQAaNmwIiUSCIUOG5Lm8Z8+eYeTIkbCzs4NUKkWlSpXQpEkTHD58WNEmt8NwEokE48ePx4YNG+Di4gJDQ0PUrVsX+/btU2qXnp6O1atXY8CAAUp7lQq6HQCAl5cXXFxcsHz58gJ9RmWaIMpHZmamMDQ0FA0bNizwPPb29qJKlSrC1dVVrF+/Xhw6dEj07t1bABAnTpxQtIuOjhZ2dnbC3t5erFixQhw+fFj89NNPQiqViiFDhijaRUZGCgDCzs5OfPTRR2LHjh1i+/bton79+kJXV1ecOXNG0dbDw0M0adIkR03169cX9evXVzx3cnISNWrUEBs2bBAnTpwQO3bsEJMnTxbHjh0rsX588cUXwsDAQCQkJCjVtnTpUgFAXL58+b2fa+fOnZWmpaenC0tLS2FrayuEEOL48eNCV1dXeHl5iYCAALF7927Rrl07IZFIxNatWxXzHTt2TABQ9DctLU1YW1uLgQMHKi0/IyND2Nrait69eyumNW/eXJibm4uaNWuK5cuXi6CgIDF27FgBQKxbt07RLjY2VlSuXFlUqlRJLF++XAQGBorx48cLAGLMmDGKdtnr197eXnTt2lXs27dPbNy4UVhZWYlatWoJX19fMWzYMHHw4EGxfPlyUaFCBdG1a1elOps3by6aN2+uNG3IkCFi9erVIigoSAQFBYmffvpJGBgYiBkzZrx33rxs2rRJABB//vmnEEKIjz76SFSoUEEkJSUptZs2bZqiT1999ZU4dOiQmDdvnjAyMhIeHh4iPT1d0dbe3l5UrlxZVK1aVaxZs0YcOHBADBw4UAAQc+fOVbTLXmeVK1cWn3zyidizZ4/Yt2+feP78ufj1118FANG/f3+xf/9+sX79elGtWjUhk8nErVu3hBBCyOVy0alTJ1GxYkVx//59IYQQa9asEQDEX3/9lWN9rF27Nkd/nJycxE8//SSCgoLE119/LQCI8ePHC2dnZ7Fo0SIRFBQkhg4dKgCIHTt2KOaPj48XQ4YMERs2bBBHjx4VgYGB4ssvvxRaWlpK20xwcLAwMDAQnTp1EsHBwSI4OFhcu3ZNqf9vf0ez10e7du3E7t27RUBAgPDy8hJ6enri1KlTudb/448/iqCgIDFv3jwhlUrF0KFD37veC/L5Xrt2Tfzwww+Kzy44OFjcuXMnz2W2b99eVKpUSaxcuVIcP35c7N69W/z4449K31M/Pz9hb2+vNB8A4eDgIBo0aCC2bdsmDhw4IFq0aCF0dHTE3bt3Fe1OnjwpAIgDBw4ozV/Q7SDbmDFjhIWFhZDL5e/9nMoyhiXKV0xMjAAg+vXrV+B57O3thb6+vnjw4IFiWkpKijAzMxOjRo1STBs1apSoUKGCUjshhPj9998FAMUfyew/3ra2tiIlJUXRLjExUZiZmYk2bdoopq1du1YAEGFhYYpp58+fV/ohj4uLEwDEggULSrUfly9fFgDEypUrldo1aNBAeHl55VtLdj2dOnUSGRkZIiMjQ0RGRgo/Pz8BQHz11VdCCCEaNWokLC0tlX68MzMzhbu7u6hSpYriD15uPzzTpk0Tenp64unTp4ppAQEBOcJh8+bNBQBx7tw5pfpcXV1F+/btFc+//fbbXNuNGTNGSCQSERERIYT4//Vbt25dkZWVpWi3YMECAUB069ZNaf6JEycKAEqh832BJysrS2RkZIiZM2cKc3NzpT/8hQlLrVq1Evr6+uLly5dCiP/f3lavXq3ULvvH+YsvvlCanv3jvnHjRsU0e3t7IZFIRHh4uFLbtm3bChMTE/Hq1SshxP+vs2bNmim1e/nypSJgvO3hw4dCKpWKAQMGKKbFxcWJKlWqiAYNGoiLFy8KQ0NDMWjQIKX58gtLf/zxh1LbevXqCQBi586dimkZGRmiUqVKomfPnjk+v2yZmZkiIyNDDB8+XHh4eCi9ZmRkJPz8/HLM8+42m5WVJWxtbUXt2rWVtpukpCRhaWkpGjdunKP+3377TWmZY8eOFfr6+vkGgcJ8vtnbQ0hISJ7Ly1ahQgUxceLEfNvkFZasrKxEYmKiYlpMTIzQ0tISs2bNUkybM2eOACBiYmJyLLcg20G2VatWCQDixo0b7+1TWcbDcFQi6tWrh6pVqyqe6+vro1atWkqHi/bt24eWLVvC1tYWmZmZikfHjh0BACdOnFBaZs+ePaGvr694bmxsjK5du+LkyZPIysoCAPTv3x+Wlpb4888/Fe0WL16MSpUqoW/fvgAAMzMzVK9eHXPnzsW8efMQFhaW55UixdmP2rVrw8vLC2vXrlXMe+PGDZw/fx7Dhg0ryMeKAwcOQFdXF7q6unB0dMS2bdvw2Wef4eeff8arV69w7tw5fPLJJ6hQoYJiHm1tbfj6+uLRo0eIiIjIc9nZ5zytWrVKMW3JkiWoXbs2mjVrptTW2to6xzkZderUUfpcjh49CldX1xzthgwZAiEEjh49qjS9U6dOSocLXFxcACDHicbZ0x8+fJhnX7Lfv02bNpDJZNDW1oauri5+/PFHPH/+PMdhvIKIjIzEsWPH0LNnT5iamgIAevfuDWNj41wPxQHAwIEDlZ736dMHOjo6OHbsmNJ0Nzc31K1bV2nagAEDkJiYmONqpF69eik9Dw4ORkpKSo5DPnZ2dmjVqpXSoWpzc3MEBATg4sWLaNy4MapWrVqoQyzvXh3q4uICiUSi2NYBQEdHBzVq1FDaFgBg+/btaNKkCSpUqAAdHR3o6upi9erVSoeyCiMiIgJPnjyBr6+v0nZToUIF9OrVC2fPnsXr16+V5nn3dIE6deogNTU13+2hMJ9vYTRo0AD+/v74+eefcfbsWWRkZBR43pYtWyqdOG5lZQVLS0ulz/zJkyeQSCSwsLDIMX9htgNLS0sAwOPHjwtcX1nEsET5srCwgKGhISIjIws1n7m5eY5pUqkUKSkpiudPnz7F3r17FT/+2Q83NzcAQFxcnNL81tbWOZZpbW2N9PR0JCcnK95j1KhR2Lx5M+Lj4/Hs2TNs27YNn376qeJ8K4lEgiNHjqB9+/b47bff4OnpiUqVKuHzzz9HUlJSifZj2LBhCA4Oxs2bNwEAa9euhVQqRf/+/fP5NP/fRx99hJCQEFy4cAHXr19HfHw8Fi1aBD09Pbx8+RJCCNjY2OSYz9bWFgDw/PnzPJdtZWWFvn37YsWKFcjKysLly5dx6tQpjB8/Pkfbgnwuz58/L1QtZmZmSs/19PTynZ6amppnX86fP4927doBeBP+Tp8+jZCQEHz//fcAoFRnQa1ZswZCCHzyySeIj49HfHw8MjIy0K1bN5w+fVqxTt/27jaro6MDc3PzHH3Pa9sGcn5O736m2a/n9Vm/O3/Dhg3h5uaG1NRUjBkzBkZGRnl1OYfc1oWhoaHSf2Kyp7+9fnbu3Ik+ffqgcuXK2LhxI4KDgxESEoJhw4blux7z875+y+VyvHz5Umn6u9tt9t+E/LaHwn6+BRUQEAA/Pz/89ddf8PHxgZmZGQYPHoyYmJj3zluQ719KSgp0dXWhra2d6zIKuh1kr9uifGfKEl4NR/nS1tZG69atcfDgQTx69AhVqlQptmVbWFigTp06+OWXX3J9PftHNVtuf0RiYmKgp6entCdlzJgxmD17NtasWYPU1FRkZmZi9OjRSvPZ29srLvu+desWtm3bhunTpyM9Pb3QJzMWph/9+/fHpEmT4O/vj19++QUbNmxA9+7dUbFixQK9l0wmg7e3d66vVaxYEVpaWoiOjs7xWvbJ2bn9L/NtEyZMwIYNG/DPP/8gMDAQpqamOfaOFJS5ufkH1fIhtm7dCl1dXezbt0/phzy3S9ILQi6XK054zuvKojVr1uQ4sTkmJgaVK1dWPM/MzMTz589z/NjltW0DOX8YJRKJ0vPs1/P6rN/9nKdNm4YrV67Ay8sLP/74I7p06YJq1arl2qfisnHjRjg6OiIgIECp/rS0tCIv83391tLSKvD36kPep6jbsYWFBRYsWIAFCxbg4cOH2LNnD7799lvExsYWy9XFFhYWSE9Px6tXr3INQgXdDrLH0CvJ76sm4J4leq8pU6ZACIERI0YgPT09x+sZGRk5rqwoiC5duuDq1auoXr06vL29czzeDUs7d+5U+l9oUlIS9u7di6ZNmyr978nGxga9e/fG0qVLsXz5cnTt2lXpUNq7atWqhR9++AG1a9cu0gBshelHxYoV0b17d6xfvx779u1DTExMgQ/BvY+RkREaNmyInTt3Kv0vUC6XY+PGjahSpQpq1aqV7zK8vLzQuHFjzJkzB5s2bcKQIUMKtefhba1bt8b169dzfKbZVya2bNmySMstiOzL6d/eLlJSUrBhw4YiLe/QoUN49OgRxo0bh2PHjuV4uLm5Yf369Tmu4ty0aZPS823btiEzMzPHlXvXrl3DpUuXlKZt3rwZxsbG7x1XyMfHBwYGBti4caPS9EePHuHo0aNo3bq1YlpQUBBmzZqFH374AUFBQZDJZOjbt2+u3+viJJFIFIM0ZouJiclxNRyQcw9JXpycnFC5cmVs3rxZ6QrHV69eYceOHYor5D5UYT7foqpatSrGjx+Ptm3bFtsgkM7OzgCAu3fv5nitMNvBvXv3oKWlBScnp2KpS1MxLNF7+fj4YNmyZTh8+DC8vLywdOlSnDhxAocPH8bcuXPh6uqa5zkb+cm+JL1x48ZYtmwZjh49igMHDmDp0qXo0qULHj16pNReW1sbbdu2xa5du7Bjxw60bt0aiYmJmDFjRo5lT5gwAXfv3kVUVFSOw0iXL19Gs2bNsHjxYgQGBuLo0aP44YcfcPnyZbRt27bE+zFs2DBER0dj/PjxqFKlCtq0aVPo98zLrFmz8Pz5c7Rs2RJ///039uzZg06dOuHq1av4/fffc+yVyM2ECRNw/vx5pKSkYOzYsUWu5YsvvkDlypXRuXNnrFq1Cv/++y8mTJiApUuXYsyYMe8Nbh+ic+fOSE5OxoABAxAUFIStW7eiadOmuQ59URCrV6+Gjo4OvvvuO8UwBW8/Ro0ahadPn+YYomHnzp34+uuvERQUhAULFmDUqFGoW7cu+vTpo9TO1tYW3bp1w9q1axEYGIhBgwYhKCgIP/zww3t/8E1NTTF16lTs2bMHgwcPxsGDB7Fx40a0bNkS+vr6mDZtGoA3e0YGDRqE5s2bY9q0aahYsSICAgJw6dIlfP3110X6XAqqS5cuiIiIwNixY3H06FGsW7cOH330Ua6HtmrXro3jx49j7969uHDhQp7n2WlpaeG3335DeHg4unTpgj179mD79u1o2bIl4uPjMXv27GKpvaCfb2EkJCTA09MTv//+O/bt24cTJ07g999/R2BgYJH+BuUmO5CfPXtWaXpht4OzZ8+iXr16xbKXTqOp9PRy0ijh4eHCz89PVK1aVejp6Skug/7xxx9FbGysol1ul7gLkftVR8+ePROff/65cHR0FLq6usLMzEx4eXmJ77//XiQnJwsh/v/qnDlz5ogZM2aIKlWqCD09PeHh4SEOHTqUZ70ODg7CxcUlx/SnT5+KIUOGCGdnZ2FkZCQqVKgg6tSpI+bPny8yMzNLrB/ZsrKyhJ2dnQAgvv/++zzrf1de9bzr1KlTolWrVsLIyEgYGBiIRo0aib179yq1ye1quGxpaWlCKpWKDh065Lr85s2bCzc3txzTc7ty58GDB2LAgAHC3Nxc6OrqCicnJzF37lylq5ey1+/bl8m/XeP27duVpud2xVFu62TNmjXCyclJSKVSUa1aNTFr1iyxevVqAUBERkbmO+/bnj17JvT09ET37t3zbJN9xVT2kAbZV1+FhoaKrl27igoVKghjY2PRv39/pasNhfj/9fr3338LNzc3oaenJxwcHMS8efMK9Hlk++uvv0SdOnWEnp6ekMlk4uOPP1ZciZmZmSmaN28urKysRHR0tNJ8c+fOFQDErl27hBD5Xw337NkzpXn9/PyEkZFRjlpy20Zmz54tHBwchFQqFS4uLmLVqlWK5b4tPDxcNGnSRBgaGgoAinWT1za7e/du0bBhQ6Gvry+MjIxE69atxenTp5Xa5FV/9rb09vaQl/w+33eX976r4VJTU8Xo0aNFnTp1hImJiTAwMBBOTk5i2rRpiqsfhcj7arhx48blWKa9vX2OqwibNm2qdBVfYbYDId5cWWhoaJjjKsjySCLEB4zQRqSmLl++jLp16+LPP//8oL0j5dHevXvRrVs37N+/H506dVJ1ORpp+vTpmDFjBp49e/becz0cHBzg7u6eY1BBog+1Y8cO9O3bFw8ePFA6d66gVq9ejQkTJiAqKqrc71niYTgqU+7evYujR49i5MiRsLGxyXcEXVJ2/fp1HDx4UDHS8tuXgxOR5unZsyfq16+PWbNmFXrezMxMzJkzB1OmTCn3QQlgWKIy5qeffkLbtm2RnJyM7du3F8sJnuXF2LFj0a1bN1SsWBFbtmwp0PlNRKS+JBIJVq1apRhKoTCioqIwaNAgTJ48uYSq0yw8DEdERESUD+5ZIiIiIsoHwxIRERFRPhiWiIiIiPLB250UA7lcjidPnsDY2JgnxRIREWkIIQSSkpJga2urdEPmdzEsFYMnT57Azs5O1WUQERFREURFReV771OGpWJgbGwM4M2HbWJiouJqiIiIqCASExNhZ2en+B3PC8NSMcg+9GZiYsKwREREpGHedwoNT/AmIiIiygfDEhEREVE+GJaIiIiI8sFzlkpRVlYWMjIyVF0GEQBAV1cX2traqi6DiEjtMSyVAiEEYmJiEB8fr+pSiJSYmprC2tqa44MREeWDYakUZAclS0tLGBoa8oeJVE4IgdevXyM2NhYAYGNjo+KKiIjUF8NSCcvKylIEJXNzc1WXQ6RgYGAAAIiNjYWlpSUPyRER5YEneJew7HOUDA0NVVwJUU7Z2yXPpSMiyhvDUinhoTdSR9wuiYjej2GJiIiIKB8MS1Qi7t+/D4lEgvDw8ALP4+/vD1NTU5XXoS4kEgl2796t6jKIiMo9hiXKU1RUFIYPHw5bW1vo6enB3t4eEyZMwPPnz987r52dHaKjo+Hu7l7g9+vbty9u3br1ISUXSYsWLSCRSHI8MjMzS+X9p0+fjnr16uWYHh0djY4dO5ZKDURElDeGJcrVvXv34O3tjVu3bmHLli24c+cOli9fjiNHjsDHxwcvXrzIc9709HRoa2vD2toaOjoFv+DSwMAAlpaWxVF+oY0YMQLR0dFKj8LUXhKsra0hlUpVWgMRkaoJIXDy1jPI5UJlNTAsUa7GjRsHPT09/Pvvv2jevDmqVq2Kjh074vDhw3j8+DG+//57RVsHBwf8/PPPGDJkCGQyGUaMGJHr4a89e/agZs2aMDAwQMuWLbFu3TpIJBLFYJ3vHobL3uOyYcMGODg4QCaToV+/fkhKSlK0CQwMxEcffQRTU1OYm5ujS5cuuHv3bqH7a2hoCGtra6UH8Gav08SJE5Xadu/eHUOGDFHq/6+//ophw4bB2NgYVatWxcqVK5XmefToEfr16wczMzMYGRnB29sb586dg7+/P2bMmIFLly4p9mj5+/sDyHkY7sqVK2jVqhUMDAxgbm6OkSNHIjk5WfH6kCFD0L17d/z++++wsbGBubk5xo0bxyvdiEgjZckF9l1+go4LT2HwmvM4fOOpymphWCplQgi8Ts9UyUOIgqXyFy9e4NChQxg7dqxiLJ5s1tbWGDhwIAICApSWN3fuXLi7uyM0NBRTp07Nscz79+/jk08+Qffu3REeHo5Ro0YpBa683L17F7t378a+ffuwb98+nDhxArNnz1a8/urVK0yaNAkhISE4cuQItLS00KNHD8jl8gL1tbj88ccf8Pb2RlhYGMaOHYsxY8bg5s2bAIDk5GQ0b94cT548wZ49e3Dp0iV8/fXXkMvl6Nu3LyZPngw3NzfFHq2+ffvmWP7r16/RoUMHVKxYESEhIdi+fTsOHz6M8ePHK7U7duwY7t69i2PHjmHdunXw9/dXhC8iIk2QmSXHzouP0G7+CYzfHIabMUmoINVBXHK6ymrioJSlLCUjC64/HlLJe1+f2R6Geu9f5bdv34YQAi4uLrm+7uLigpcvX+LZs2eKw2atWrXCl19+qWhz//59pXmWL18OJycnzJ07FwDg5OSEq1ev4pdffsm3FrlcDn9/fxgbGwMAfH19ceTIEcV8vXr1Umq/evVqWFpa4vr164U6X2rp0qX466+/FM9HjRqFP/74o8Dzd+rUCWPHjgUAfPPNN5g/fz6OHz8OZ2dnbN68Gc+ePUNISAjMzMwAADVq1FDMW6FCBejo6Cj2ZuVm06ZNSElJwfr162FkZAQAWLJkCbp27Yo5c+bAysoKAFCxYkUsWbIE2tracHZ2RufOnXHkyBGMGDGiwH0hIlKFzCw5doU9xpJjd/Dg+WsAgMxAF8OaOGJIYwfIDHVVVhvDEhVa9h6lt8fo8fb2zneeiIgI1K9fX2lagwYN3vteDg4OiqAEvLktR/YtOoA3e56mTp2Ks2fPIi4uTrFH6eHDh4UKSwMHDlTa01XYq/Lq1Kmj+LdEIoG1tbWizvDwcHh4eCiCUlHcuHEDdevWVQQlAGjSpAnkcjkiIiIUYcnNzU1pJG4bGxtcuXKlyO9LRFTScgtJZkZ6+LSpI3wb2cNYX3UhKRvDUikz0NXG9ZntVfbeBVGjRg1IJBJcv34d3bt3z/H6zZs3UbFiRVhYWCimvf0jnhshRI4BEAtyWFBXV/lLIpFIlA6xde3aFXZ2dli1ahVsbW0hl8vh7u6O9PTC7a6VyWRKe3uyaWlp5agzt3OA8qvz3UOZRZHb5/f2exWkDiIidZKZJcfu8CdYfPS2IiRZVNDDqGbVMbBR1QIdCSkt6lNJOSGRSNRqA8iNubk52rZti6VLl+KLL75Q+rGPiYnBpk2bMHjw4EKN/uzs7IwDBw4oTbtw4cIH1fn8+XPcuHEDK1asQNOmTQEA//333wct812VKlVCdHS04nlWVhauXr2Kli1bFngZderUwV9//YUXL17kundJT08PWVlZ+S7D1dUV69atw6tXrxTB9PTp09DS0kKtWrUKXAsRkarJ5QL7rkRjweFbuPfsFQD1DUnZeII35WrJkiVIS0tD+/btcfLkSURFRSEwMBBt27ZF5cqV33uu0btGjRqFmzdv4ptvvsGtW7ewbds2pau+iqJixYowNzfHypUrcefOHRw9ehSTJk0q0rLy0qpVK+zfvx/79+/HzZs3MXbsWMXVewXVv39/WFtbo3v37jh9+jTu3buHHTt2IDg4GMCbQ42RkZEIDw9HXFwc0tLScixj4MCB0NfXh5+fH65evYpjx47hs88+g6+vr+IQHBGROhNC4NC1GHRadAqfbwnDvWevUNFQF1M6OuPk1y0xolk1tQxKAMMS5aFmzZq4cOECqlevjr59+6J69eoYOXIkWrZsieDg4EKff+Po6Ii///4bO3fuRJ06dbBs2TLFOUJFHUtIS0sLW7duRWhoKNzd3fHFF18oTiAvLsOGDYOfnx8GDx6M5s2bw9HRsVB7lQAohmCwtLREp06dULt2bcyePVtxblGvXr3QoUMHtGzZEpUqVcKWLVtyLMPQ0BCHDh3CixcvUL9+fXzyySdo3bo1lixZUiz9JCIqSWfuxqH70jMYtSEUN2OSYKyvg8lta+HUN60wqnl1tQ1J2SSioNeTU54SExMhk8mQkJAAExMTpddSU1MRGRkJR0dH6Ovrq6hC9fTLL79g+fLliIqKUnUp5Ra3TyIqSVceJeC3Qzdx6nYcgDfnzg5t4oCRzarB1FBPxdXl//v9NvWOclSmLF26FPXr14e5uTlOnz6NuXPn5hgniIiINN/9uFeYeygC+6+8OedTV1uCgQ3tMa5lDVQy1rw7EzAsUam5ffs2fv75Z7x48QJVq1bF5MmTMWXKFFWXRURExSQuOQ2LjtzG5nMPkSkXkEiAHvUq44u2tWBnZqjq8oqMYYlKzfz58zF//nxVl0FERMXsdXom/joViRUn7uJV+pure1s4VcI3HZzhYpP34S1NwbBERERERZIlF9hx8RH++DcCTxPfXMlbu7IMUzo6o3ENi/fMrTkYlkoJz6MndcTtkoiK6vSdOPy8/wZuRCcCAKpUNMBX7Z3QtY4ttLSKNiSMumJYKmHZIyq/fv26WEZyJipOr1+/GTX33ZG/iYjycvdZMn7dfwNHbr65pZOxvg4+a1UDfo0dINUp2J0iNI3GhaWlS5di7ty5iI6OhpubGxYsWKAYvfldQ4YMwbp163JMd3V1xbVr1wAA/v7+GDp0aI42KSkpxXIptba2NkxNTRX3CTM0NCzyIIxExUUIgdevXyM2NhampqZK95MjIspNwusMLDxyG+uD7yNTLqCjJcGgRvb4vHVNmBmpfhiAkqRRYSkgIAATJ07E0qVL0aRJE6xYsQIdO3bE9evXUbVq1RztFy5ciNmzZyueZ2Zmom7duujdu7dSOxMTE0RERChNK84xZ7LvJv/2DWCJ1IGpqali+yQiyk1mlhxbzj/EvKBbePn6zb0xWztb4rvOLqheqYKKqysdGhWW5s2bh+HDh+PTTz8FACxYsACHDh3CsmXLMGvWrBztZTIZZDKZ4vnu3bvx8uXLHHuSsu8SX1IkEglsbGxgaWmZ601YiVRBV1eXe5SIKF9n7sZhxp7riHiaBACoZVUBP3R2RbNalVRcWenSmLCUnp6O0NBQfPvtt0rT27VrhzNnzhRoGatXr0abNm1gb2+vND05ORn29vbIyspCvXr18NNPP8HDwyPP5aSlpSndvysxMbFA76+trc0fJyIiUnuP41Pw6/4bikElTQ11MbltLfRvUBU62uXvTmkaE5bi4uKQlZWV46ahVlZWiImJee/80dHROHjwIDZv3qw03dnZGf7+/qhduzYSExOxcOFCNGnSBJcuXULNmjVzXdasWbMwY8aMoneGiIhIDaVmZGHFiXtYduIOUjPk0JIAgxrZY1LbWmpxexJV0ZiwlO3dk6OFEAU6Ydrf3x+mpqbo3r270vRGjRqhUaNGiudNmjSBp6cnFi9ejEWLFuW6rClTpijd3T4xMRF2dnaF6AUREZF6OXLjKabvvYaoFykAgIaOZpjeza1MDCr5oTQmLFlYWEBbWzvHXqTY2Ngce5veJYTAmjVr4OvrCz29/JOxlpYW6tevj9u3b+fZRiqVQirVvHvbEBERvevh89eYsfeaYigAaxN9fN/ZBV3q2PDq7f/RmAOPenp68PLyQlBQkNL0oKAgNG7cON95T5w4gTt37mD48OHvfR8hBMLDw2FjY/NB9RIREamz1IwsLDh8C23mn8CRm7HQ1ZZgdPPqODK5ObrWtWVQeovG7FkCgEmTJsHX1xfe3t7w8fHBypUr8fDhQ4wePRrAm8Njjx8/xvr165XmW716NRo2bAh3d/ccy5wxYwYaNWqEmjVrIjExEYsWLUJ4eDj+/PPPUukTERFRaTtx6xl+/OcqHjx/MzDtRzUsML2bG2pYlo+hAApLo8JS37598fz5c8ycORPR0dFwd3fHgQMHFFe3RUdH4+HDh0rzJCQkYMeOHVi4cGGuy4yPj8fIkSMRExMDmUwGDw8PnDx5Eg0aNCjx/hAREZWmmIRU/LTvuuIqNysTKaZ2cUXn2jzklh+J4M2hPlhiYiJkMhkSEhJgYsIT4YiISL1kyQXWB9/H74ci8Co9C1oSYEhjR3zRtiaM9cvv7Y4K+vutUXuWiIiIqHCuPErAd7uu4MrjBABAPTtT/NLDHW62svfMSdkYloiIiMqg5LRMzPv3FvzPREIu3tzw9psOzhjQoCq0tHjIrTAYloiIiMqYIzeeYuruq3iSkAoA6FLHBj92cYWlSfHd97Q8YVgiIiIqI54lpWHG3mvYd/nNCdxVKhrg5+7uaOFkqeLKNBvDEhERkYYTQmB76CP8sv8GElIyoCUBPm1aDRPb1IShHn/qPxQ/QSIiIg328PlrTNl1GafvPAcAuNmaYHbPOqhdhSdwFxeGJSIiIg2UJRfwP/NmOICUjCxIdbQwqW0tDP/IETraGnODDo3AsERERKRhbj9Nwtc7LiPsYTyANze9ndOrDhwsjFRbWBnFsERERKQhMrPkWHHyHhYevo30LDkqSHXwXScX9Ktvx+EAShDDEhERkQa4GZOIr7ZfVgwu2crZEr/0cIeNzEDFlZV9DEtERERqLCNLjmXH72Lx0dvIyBKQGehiWldX9PCozPu5lRKGJSIiIjV1MyYRk7ddwrUniQCAtq5W+KW7OweXLGUMS0RERGom+9ykBYdvISNLwNRQFzO6uaFbXVvuTVIBhiUiIiI1cic2CZO3XcKlR2/OTWrjYoVfe7rD0ph7k1SFYYmIiEgNZMkF1vwXibn/RiA9Uw4TfR1M7+bGc5PUAMMSERGRikW9eI3J2y/hfOQLAEALp0qY3bMOrGXcm6QOGJaIiIhURAiBrSFR+HnfdbxKz4KRnjZ+6OKKfvXtuDdJjTAsERERqUBsUiq+3XEFR2/GAgAaOJjh9951UdXcUMWV0bsYloiIiErZoWsxmLLzCl68Soeetha+bF8Lwz+qBm2Owq2WGJaIiIhKSXJaJmbuvYZtFx4BAFxsTLCgbz04WRuruDLKD8MSERFRKQh98AITA8IR9SIFEgkwslk1TGpbC1IdbVWXRu/BsERERFSCMrLkWHzkNpYcuwO5ACqbGmBen7poWM1c1aVRATEsERERlZD7ca8wISAcl6LiAQA9PCpjxsduMNHXVW1hVCgMS0RERMVMCIHtFx5h+t5reJ2eBRN9Hfzcoza61bVVdWlUBAxLRERExSjhdQam7LqMA1diAACNqplhXp96sDU1UHFlVFQMS0RERMXk3L3n+CIgHE8SUqGjJcHkdk4Y2YxDAmg6hiUiIqIPlJklx8Ijt/Hn/07idjA3xMJ+HqhrZ6rq0qgYMCwRERF9gKgXrzFhaxguPowHAPT2qoLp3dxgJOVPbFnBNUlERFRE+y9H49udl5GUmgljfR382qM2uvIk7jKHYYmIiKiQXqdnYube69gaEgUA8KhqikX9PGBnxvu6lUUMS0RERIVwMyYR4zeH4U5sMiQSYFyLGpjQpiZ0tbVUXRqVEIYlIiKiAhBCYPP5h5i59zrSMuWwNJZiQd96aFzDQtWlUQljWCIiInqPxNQMTNlxBfuvRAMAWjhVwh+968K8glTFlVFpYFgiIiLKx6WoeIzfchFRL1KgoyXB1x2c8OlH1aDFsZPKDYYlIiKiXAghsPb0fcw6eAMZWQJVKhpgcX8PeFStqOrSqJQxLBEREb0j4XUGvvr7Ev69/hQA0MHNGnM+qQOZAW+AWx4xLBEREb0lPCoe4zZdxOP4FOhpa+H7zi4Y7GMPiYSH3corhiUiIiLkPOxW1cwQfw7wRO0qMlWXRirGsEREROVeYmoGvt5+GYHXYgAAHd3fHHYz0edhNwI0bgStpUuXwtHREfr6+vDy8sKpU6fybHv8+HFIJJIcj5s3byq127FjB1xdXSGVSuHq6opdu3aVdDeIiEhNXH2cgC6L/kPgtRjoakswvasrlg70ZFAiBY0KSwEBAZg4cSK+//57hIWFoWnTpujYsSMePnyY73wRERGIjo5WPGrWrKl4LTg4GH379oWvry8uXboEX19f9OnTB+fOnSvp7hARkQoJIbDp3AP0XHoGD1+8RmVTA/w9ujGGNHHk+UmkRCKEEKouoqAaNmwIT09PLFu2TDHNxcUF3bt3x6xZs3K0P378OFq2bImXL1/C1NQ012X27dsXiYmJOHjwoGJahw4dULFiRWzZsqVAdSUmJkImkyEhIQEmJiaF6xQREZW61+mZ+H7XVewKewwAaONihT9614XMkHuTypOC/n5rzJ6l9PR0hIaGol27dkrT27VrhzNnzuQ7r4eHB2xsbNC6dWscO3ZM6bXg4OAcy2zfvn2+y0xLS0NiYqLSg4iINMOd2GR0//M0doU9hraWBFM6OmPVYC8GJcqTxoSluLg4ZGVlwcrKSmm6lZUVYmJicp3HxsYGK1euxI4dO7Bz5044OTmhdevWOHnypKJNTExMoZYJALNmzYJMJlM87OzsPqBnRERUWvZeeoKPl/yHW0+TUclYis2fNsSo5tV52I3ypXFXw727QQsh8tzInZyc4OTkpHju4+ODqKgo/P7772jWrFmRlgkAU6ZMwaRJkxTPExMTGZiIiNRYeqYcsw7ewNrT9wEAjaqZYVF/D1ga66u2MNIIGhOWLCwsoK2tnWOPT2xsbI49Q/lp1KgRNm7cqHhubW1d6GVKpVJIpbx5IhGRJohJSMW4zRcR+uAlAGB08+r4sl0t6GhrzMEVUjGN2VL09PTg5eWFoKAgpelBQUFo3LhxgZcTFhYGGxsbxXMfH58cy/z3338LtUwiIlJPZ+7GocviUwh98BLGUh2s9PXCtx2dGZSoUDRmzxIATJo0Cb6+vvD29oaPjw9WrlyJhw8fYvTo0QDeHB57/Pgx1q9fDwBYsGABHBwc4ObmhvT0dGzcuBE7duzAjh07FMucMGECmjVrhjlz5uDjjz/GP//8g8OHD+O///5TSR+JiOjDCSGw8uQ9zAm8CbkAnK2NsXyQFxwsjFRdGmkgjQpLffv2xfPnzzFz5kxER0fD3d0dBw4cgL29PQAgOjpaacyl9PR0fPnll3j8+DEMDAzg5uaG/fv3o1OnToo2jRs3xtatW/HDDz9g6tSpqF69OgICAtCwYcNS7x8REX24pNQMfPXWaNw9PSvjl+61YaCnreLKSFNp1DhL6orjLBERqYc7sUkYtSEUd5+9gq62BNO6umFgw6q82o1yVdDfb43as0RERJSXA1ei8dX2S3iVngVrE30sG+QJj6oVVV0WlQEMS0REpNEys+SY+28EVpy4BwDwqWaOxQM8YFGBVy1T8WBYIiIijfXiVTo+23IRp+88BwCMbFYNX7d34tVuVKwYloiISCNdfZyAURtC8Tg+BYZ62vjtkzroUsdW1WVRGcSwREREGmdH6CN8t+sK0jLlcDA3xApfbzhZG6u6LCqjGJaIiEhjZGTJ8cv+G/A/cx8A0MrZEvP71oPMgDfBpZLDsERERBohLjkN4zZdxLnIFwCAz1vXxMTWNaGlxWEBqGQxLBERkdq7/CgeozeE4klCKipIdfBHn7po72at6rKonGBYIiIitbYj9BGm7LqC9Ew5qlkYYeVgL9Sw5PlJVHoYloiISC1lZsnx64GbWHM6EgDQ2tkS8/vVg4k+z0+i0sWwREREauflq3SM23wRZ+6+GT/p81Y1MLFNLZ6fRCrBsERERGrlRnQiRqy/gEcv34yfNK9PXXRwt1F1WVSOMSwREZHaOHglGpO2XUJKRhaqmhli1WCOn0Sqx7BEREQqJ5cLLDh8C4uO3gEAfFTDAksGeMDUUE/FlRExLBERkYolp2Xii4BwBF1/CgAY/pEjpnR05v3dSG0wLBERkco8eP4KI9ZfwK2nydDT0cKvPWrjE68qqi6LSAnDEhERqcSZO3EYu/ki4l9nwNJYihW+XvCoWlHVZRHlwLBERESlSgiBDWcfYMbe68iSC9StIsPKwd6wMtFXdWlEuWJYIiKiUpOeKce0Pdew5fxDAEAPj8qY1bM29HW1VVwZUd4YloiIqFQ8T07DmE0XcT7yBSQS4NsOzhjZrBokEg40SeqNYYmIiErczZhEfLruzUCTFaQ6WNzfAy2dLVVdFlGBMCwREVGJCrr+FBO3huFVehbszQ3x12Bv1LTiQJOkORiWiIioRAghsPzEPfx26CaEABpXN8efAzxR0YgDTZJmYVgiIqJil5qRhe92XsHOsMcAgEGNqmJaVzfocqBJ0kAMS0REVKyeJaVh5IYLCHsYD20tCaZ3dYWvj4OqyyIqMoYlIiIqNtefJOLTdSF4kpAKE30dLB3ohY9qWqi6LKIPwrBERETF4t9rMZgYEI7X6VlwtDDCaj9vVKtUQdVlEX0whiUiIvogQgisOHkPcwLfnMjdpIY5lg7wgsxQV9WlERULhiUiIiqytMwsfL/rKv4OfQSAJ3JT2cSwRERERfLiVTpGbwjF+fsvoCUBpnV1g19jB1WXRVTsGJaIiKjQbj9NwrB1IYh6kQJjqQ6WDPRE81qVVF0WUYlgWCIiokI5eesZxm26iKS0TFQ1M8RqP47ITWUbwxIRERXYhrMPMH3PNWTJBeo7VMTyQV4wryBVdVlEJYphiYiI3iszS46f99+A/5n7AICenpUxq2dtSHW0VVsYUSlgWCIionwlpWbg8y1hOBbxDADwVXsnjG1RHRKJRMWVEZUOhiUiIsrT4/gUDPcPwc2YJOjramFen3roVNtG1WURlSqGJSIiylV4VDw+XXcBcclpqGQsxV+DvVHXzlTVZRGVOoYlIiLK4cCVaHwREI60TDmcrY2xekh9VDY1UHVZRCrBsERERApCCCw7cRe/BUYAAFo6VcLiAZ6oIOXPBZVfGjce/dKlS+Ho6Ah9fX14eXnh1KlTebbduXMn2rZti0qVKsHExAQ+Pj44dOiQUht/f39IJJIcj9TU1JLuChGRWknPlOObHZcVQWlIYwesGuzNoETlnkaFpYCAAEycOBHff/89wsLC0LRpU3Ts2BEPHz7Mtf3JkyfRtm1bHDhwAKGhoWjZsiW6du2KsLAwpXYmJiaIjo5Weujr65dGl4iI1ELC6wwMWXse2y48gpYEmNHNDdO7uUGH93gjgkQIIVRdREE1bNgQnp6eWLZsmWKai4sLunfvjlmzZhVoGW5ubujbty9+/PFHAG/2LE2cOBHx8fFFrisxMREymQwJCQkwMTEp8nKIiFTh4fPXGOp/HnefvYKRnjYWD/BAK2crVZdFVOIK+vutMf9lSE9PR2hoKNq1a6c0vV27djhz5kyBliGXy5GUlAQzMzOl6cnJybC3t0eVKlXQpUuXHHue3pWWlobExESlBxGRJgp98BLdl57G3WevYCPTx/bRjRmUiN6hMWEpLi4OWVlZsLJS/hJbWVkhJiamQMv4448/8OrVK/Tp00cxzdnZGf7+/tizZw+2bNkCfX19NGnSBLdv385zObNmzYJMJlM87OzsitYpIiIV2nvpCfqvOosXr9LhXtkEu8c1gast944TvUtjwlK2d0eMFUIUaBTZLVu2YPr06QgICIClpaVieqNGjTBo0CDUrVsXTZs2xbZt21CrVi0sXrw4z2VNmTIFCQkJikdUVFTRO0REVMqEEPjz2B18tiUM6ZlytHGxwrZRPrAy4bmaRLnRmEscLCwsoK2tnWMvUmxsbI69Te8KCAjA8OHDsX37drRp0ybftlpaWqhfv36+e5akUimkUt44kog0T0aWHN/vuoJtFx4BAIY1ccT3nV2grcVblxDlRWP2LOnp6cHLywtBQUFK04OCgtC4ceM859uyZQuGDBmCzZs3o3Pnzu99HyEEwsPDYWPD4fyJqGxJSMl5xduPXV0ZlIjeQ2P2LAHApEmT4OvrC29vb/j4+GDlypV4+PAhRo8eDeDN4bHHjx9j/fr1AN4EpcGDB2PhwoVo1KiRYq+UgYEBZDIZAGDGjBlo1KgRatasicTERCxatAjh4eH4888/VdNJIqIS8OjlawxdG4Lbsckw1NPGEl7xRlRgGhWW+vbti+fPn2PmzJmIjo6Gu7s7Dhw4AHt7ewBAdHS00phLK1asQGZmJsaNG4dx48Yppvv5+cHf3x8AEB8fj5EjRyImJgYymQweHh44efIkGjRoUKp9IyIqKZcfxWOY/5t7vFmZSLHarz7cK8tUXRaRxtCocZbUFcdZIiJ19e+1GEzYGo6UjCw4Wxtj7dD6sJHxHm9EQMF/vzVqzxIRERXc2tORmLnvOoQAmtWqhD8HeMBYX1fVZRFpHIYlIqIyJksu8PP+61h7+j4AoH+Dqpj5sRt0eesSoiJhWCIiKkNS0rMwYWsY/r3+FADwbUdnjGpWrUDj0RFR7hiWiIjKiGdJafh0XQguPUqAno4W/uhdF13r2qq6LCKNx7BERFQG3IlNwpC1IXj0MgUVDXWxarA3vB3M3j8jEb0XwxIRkYY7e+85Rq6/gMTUTDiYG2Lt0AZwtDBSdVlEZQbDEhGRBvsn/DG+2n4Z6VlyeFY1xV9+9WFmpKfqsojKFIYlIiINJITA0uN3MfdQBACgo7s15vetB31dbRVXRlT2MCwREWmYzCw5pv5zFVvORwEARjR1xJSOLtDiPd6ISgTDEhGRBklOy8S4TRdx4tYzaEmAaV3d4NfYQdVlEZVpDEtERBriaWIqhq4NwfXoROjramFxf0+0deXNcIlKGsMSEZEGiIhJwtC15/EkIRUWFfTwl1991LMzVXVZROUCwxIRkZo7cycOozaGIik1E9UqGcF/SANUNTdUdVlE5QbDEhGRGtsV9ghf/30ZGVkC9R0qYqWvNypyaACiUsWwRESkhoQQ+PPYHfz+7y0AQOc6Nvijd10ODUCkAgxLRERqJjNLjh92X8XWkDdDA4xqVg3fdHDm0ABEKsKwRESkRl6lZWLsW0MDTO/mhsE+Dqoui6hcY1giIlITsUmpGOYfgquP3wwNsKifB9q5Wau6LKJyj2GJiEgN3IlNxpC15/HoZQrMjfTwl583PKpWVHVZRASGJSIilTsf+QIj1l9AQkoGHMwNsW5YA9ibG6m6LCL6H4YlIiIV2n85Gl9sC0d6phyeVU3xl199mHFoACK1wrBERKQCQgis/i8SP++/AQBo72aFhf08ODQAkRpiWCIiKmVZcoGf91/H2tP3AQBDGjtgahdXaHNoACK1xLBERFSKUjOyMHFrOAKvxQAAvu/kgk+bOkIiYVAiUlcMS0REpeTlq3R8uv4CQh+8hJ62Fv7oUxdd69qquiwieg+GJSKiUhD14jX81pzHvbhXMNHXwcrB3mhUzVzVZRFRATAsERGVsMuP4jHMPwRxyemobGoA/6H1UdPKWNVlEVEBMSwREZWgYzdjMW7zRbxOz4KLjQn8h9aHlYm+qssiokJgWCIiKiFbzz/E97uvIksu0LSmBZYO9ISxvq6qyyKiQmJYIiIqZkIIzD98G4uO3AYA9PKsgtm9akNXW0vFlRFRUTAsEREVo4wsOabsvIK/Qx8BAD5vVQNftK3FoQGINBjDEhFRMUlOy8SYjaE4dTsOWhLg5+61MaBhVVWXRUQfiGGJiKgYxCamYqh/CK49SYSBrjaWDPBAaxcrVZdFRMWAYYmI6APdiU2C35oQPI5PgbmRHtYMqY+6dqaqLouIikmhw1JERAS2bNmCU6dO4f79+3j9+jUqVaoEDw8PtG/fHr169YJUKi2JWomI1E7I/Rf4dN0FJKRkwMHcEOuGNYC9uZGqyyKiYiQRQoiCNAwLC8PXX3+NU6dOoXHjxmjQoAEqV64MAwMDvHjxAlevXsWpU6eQmJiIr7/+GhMnTiw3oSkxMREymQwJCQkwMTFRdTlEVEoOXonGhIBwpGfKUc/OFKv9vGFeoXz83SMqCwr6+13gPUvdu3fHV199hYCAAJiZmeXZLjg4GPPnz8cff/yB7777rnBVExFpiLWnIzFz33UIAbRxscLi/h4w0NNWdVlEVAIKvGcpPT0denp6BV5wYdtrMu5ZIio/5HKBWQdvYNWpSADAoEZVMaObO7S1ODQAkaYp9j1LBQ0+r1+/hqGhYbkJSkRUfqRlZuHL7Zex99ITAMDXHZwwpnl1jqFEVMYVaTjZFi1a4NGjRzmmnzt3DvXq1fvQmvK1dOlSODo6Ql9fH15eXjh16lS+7U+cOAEvLy/o6+ujWrVqWL58eY42O3bsgKurK6RSKVxdXbFr166SKp+INFRCSgYGrz6PvZeeQFdbgvl962JsixoMSkTlQJHCkomJCerUqYOtW7cCAORyOaZPn45mzZqhW7duxVrg2wICAjBx4kR8//33CAsLQ9OmTdGxY0c8fPgw1/aRkZHo1KkTmjZtirCwMHz33Xf4/PPPsWPHDkWb4OBg9O3bF76+vrh06RJ8fX3Rp08fnDt3rsT6QUSa5Ul8CnovP4NzkS9QQaoD/6EN0MOjiqrLIqJSUuBzlt61fPlyfPnll+jWrRvu37+Phw8fwt/fH23atCnuGhUaNmwIT09PLFu2TDHNxcUF3bt3x6xZs3K0/+abb7Bnzx7cuHFDMW306NG4dOkSgoODAQB9+/ZFYmIiDh48qGjToUMHVKxYEVu2bClQXTxniajsuhmTiCFrQhCTmApLYyn8hzaAqy2/50RlQUF/v4t8V8fRo0fjs88+w9atW3HhwgVs27atRINSeno6QkND0a5dO6Xp7dq1w5kzZ3KdJzg4OEf79u3b48KFC8jIyMi3TV7LBIC0tDQkJiYqPYio7DlzJw69lwUjJjEVNS0rYNe4JgxKROVQkcLSy5cv0atXLyxbtgwrVqxAnz590K5dOyxdurS461OIi4tDVlYWrKyUbx9gZWWFmJiYXOeJiYnJtX1mZibi4uLybZPXMgFg1qxZkMlkioednV1RukREauyf8MfwW3seSWmZaOBohr9HN0ZlUwNVl0VEKlCksOTu7o6nT58iLCwMI0aMwMaNG7F69WpMnToVnTt3Lu4albx7MqUQIt8TLHNr/+70wi5zypQpSEhIUDyioqIKXD8RqTchBJafuIsJW8ORkSXQuY4N1g9rAJmhrqpLIyIVKVJYGj16NE6ePAlHR0fFtL59++LSpUtIT08vtuLeZmFhAW1t7Rx7fGJjY3PsGcpmbW2da3sdHR2Ym5vn2yavZQKAVCqFiYmJ0oOINF+WXGD6nmuYffAmAGD4R45Y3M8D+rocbJKoPCtSWJo6dSq0tHLOWqVKFQQFBX1wUbnR09ODl5dXjuUHBQWhcePGuc7j4+OTo/2///4Lb29v6Orq5tsmr2USUdmUmpGFsZtCsS74ASQS4IfOLpjaxRVaHGySqNwrcFjK6/L8vDx+/LjQxbzPpEmT8Ndff2HNmjW4ceMGvvjiCzx8+BCjR48G8Obw2ODBgxXtR48ejQcPHmDSpEm4ceMG1qxZg9WrV+PLL79UtJkwYQL+/fdfzJkzBzdv3sScOXNw+PBhTJw4sdjrJyL19PJVOgasOotD155CT1sLS/p74tOm1VRdFhGpiQKHpfr162PEiBE4f/58nm0SEhKwatUquLu7Y+fOncVS4Nv69u2LBQsWYObMmahXrx5OnjyJAwcOwN7eHgAQHR2tFOocHR1x4MABHD9+HPXq1cNPP/2ERYsWoVevXoo2jRs3xtatW7F27VrUqVMH/v7+CAgIQMOGDYu9fiJSP1EvXqPXsjO4+DAeJvo62DC8ATrXsVF1WUSkRgo8ztKLFy/w66+/Ys2aNdDV1YW3tzdsbW2hr6+Ply9f4vr167h27Rq8vb3xww8/oGPHjiVdu9rgOEtEmunKowQM9Q9BXHIabGX6WDesAWpaGau6LCIqJQX9/S5wWLp8+TLc3NyQkZGBgwcP4uTJk7h//z5SUlJgYWEBDw8PtG/fHu7u7sXWCU3BsESkeY5FxGLcpot4nZ4FFxsT+A+tDysTfVWXRUSlqNjDUvaVaJUqVUK1atUQEhKiuKKsvGNYItIs20KiMGXXFWTJBT6qYYFlgzxhrM+hAYjKm2IfwdvU1BT37t0DANy/fx9yufzDqyQiKkVCCCw4fAtf77iMLLlAT4/KWDOkPoMSEeVLp6ANe/XqhebNm8PGxgYSiQTe3t7Q1s597JHsUEVEpC4ysuT4YddVBFx4M4jsuJbV8WU7p3wHoCUiAgoRllauXImePXvizp07+PzzzzFixAgYG/NESCJSf6/SMjFu80Ucj3gGLQkw82N3DGpkr+qyiEhDFDgsAUCHDh0AAKGhoZgwYQLDEhGpvWdJaRjmH4IrjxOgr6uFxf090dY17xH6iYjeVaiwlG3t2rXFXQcRUbG7+ywZQ9aeR9SLFJgZ6WG1nzc8qlZUdVlEpGGKFJaIiNRd6IMXGL7uAuJfZ8De3BD+QxvA0cJI1WURkQZiWCKiMifwajQmbA1HWqYcde1MsdrPGxYVpKoui4g0FMMSEZUp/qcjMWPfdQgBtHGxxKL+HjDU4586Iio6/gUhojJBLheYdfAGVp2KBAAMbFgVM7q5QUe7wMPJERHlimGJiDReakYWJm+/hP2XowEAX7V3wtgW1TmGEhEVC4YlItJo8a/TMXJ9KM7ffwFdbQl++6QOenhUUXVZRFSGMCwRkcZ69PI1hqwNwZ3YZBhLdbDC1wuNa1iouiwiKmMYlohII119nICh/iF4lpQGaxN9+A+rD2dr3siaiIofwxIRaZzjEbEYu+kiXqdnwdnaGGuH1oeNzEDVZRFRGcWwREQaJSDkIb7bdRVZcoEmNcyxbJAXTPR1VV0WEZVhDEtEpBGEEJgfdAuLjt4BAPT0qIzZvepAT4dDAxBRyWJYIiK1l54px5SdV7Dj4iMAwGetamBS21ocGoCISgXDEhGptaTUDIzZeBH/3YmDtpYEP3d3R/8GVVVdFhGVIwxLRKS2ohNSMHRtCG7GJMFQTxt/DvBES2dLVZdFROUMwxIRqaUb0YkYujYEMYmpqGQsxdoh9eFeWabqsoioHGJYIiK1c/pOHEZvCEVSWiZqWFbA2iH1YWdmqOqyiKicYlgiIrXyd+gjfLvjMjLlAg0czbDK1xsyQw4NQESqw7BERGpBCIFFR+5g/uFbAIBudW0xt3cdSHW0VVwZEZV3DEtEpHIZWW+GBvg79M3QAGNbVMeX7ZygpcWhAYhI9RiWiEilElMzMG7TRZy6HQctCfBTd3cMbGiv6rKIiBQYlohIZZ7Ep2CY//8PDbBkgAdaOVupuiwiIiUMS0SkEteeJGCYfwieJqahkrEUa/zqo3YVDg1AROqHYYmISt3xiFiM23QRr9KzUMuqAtYObYDKpgaqLouIKFcMS0RUqracf4gfdl9FllygcXVzLBvkBZkBhwYgIvXFsEREpUIuF5j7bwSWHb8LAOjpWRmze9aBno6WiisjIsofwxIRlbjUjCx8uf0S9l2OBgB80aYWPm9dAxIJhwYgIvXHsEREJerlq3SMWH8BFx68hK62BLN71kEvryqqLouIqMAYloioxNyPe4Wh/iGIjHsFY30drBjkhcY1LFRdFhFRoTAsEVGJuHD/BUasv4CXrzNQ2dQA/kPro6aVsarLIiIqNIYlIip2ey89weTtl5CeKUedKjL85ecNS2N9VZdFRFQkDEtEVGyEEFh24i5+C4wAALR1tcLCfvVgqMc/NUSkufgXjIiKRUaWHFN3X8XWkCgAwLAmjvi+swu0eTNcItJwGjPAycuXL+Hr6wuZTAaZTAZfX1/Ex8fn2T4jIwPffPMNateuDSMjI9ja2mLw4MF48uSJUrsWLVpAIpEoPfr161fCvSEqWxJTMzB0bQi2hkRBSwJM7+qKH7u6MigRUZmgMWFpwIABCA8PR2BgIAIDAxEeHg5fX988279+/RoXL17E1KlTcfHiRezcuRO3bt1Ct27dcrQdMWIEoqOjFY8VK1aUZFeIypRHL1+j19Iz+O9OHAz1tLFqsDeGNHFUdVlERMVGIw7D3bhxA4GBgTh79iwaNmwIAFi1ahV8fHwQEREBJyenHPPIZDIEBQUpTVu8eDEaNGiAhw8fomrVqorphoaGsLa2LtlOEJVBl6LiMXzdBcQlp8HKRIrVfvXhXpk3wyWiskUj9iwFBwdDJpMpghIANGrUCDKZDGfOnCnwchISEiCRSGBqaqo0fdOmTbCwsICbmxu+/PJLJCUl5buctLQ0JCYmKj2IypvAq9HouzIYcclpcLExwe5xTRiUiKhM0og9SzExMbC0tMwx3dLSEjExMQVaRmpqKr799lsMGDAAJiYmiukDBw6Eo6MjrK2tcfXqVUyZMgWXLl3KsVfqbbNmzcKMGTMK3xGiMkAIgZUn72HWwZsAgJZOlbB4gCcqSDXizwkRUaGpdM/S9OnTc5xc/e7jwoULAJDrPaSEEAW6t1RGRgb69esHuVyOpUuXKr02YsQItGnTBu7u7ujXrx/+/vtvHD58GBcvXsxzeVOmTEFCQoLiERUVVcieE2mmjCw5vtt1RRGU/HzssWqwN4MSEZVpKv0LN378+Pdeeebg4IDLly/j6dOnOV579uwZrKys8p0/IyMDffr0QWRkJI4ePaq0Vyk3np6e0NXVxe3bt+Hp6ZlrG6lUCqlUmu9yiMqahJQMjNt0Ef/diYOWBJjaxRVDeSI3EZUDKg1LFhYWsLB4/32ifHx8kJCQgPPnz6NBgwYAgHPnziEhIQGNGzfOc77soHT79m0cO3YM5ubm732va9euISMjAzY2NgXvCFEZ9/D5awxbF4I7sckw1NPG4v4eaO2S/39UiIjKCokQQqi6iILo2LEjnjx5orisf+TIkbC3t8fevXsVbZydnTFr1iz06NEDmZmZ6NWrFy5evIh9+/Yp7YEyMzODnp4e7t69i02bNqFTp06wsLDA9evXMXnyZBgYGCAkJATa2toFqi0xMREymQwJCQnv3XNFpGlCH7zAiPWhePEqHdYm+vjLz5snchNRmVDQ32+NOdFg06ZN+Pzzz9GuXTsAQLdu3bBkyRKlNhEREUhISAAAPHr0CHv27AEA1KtXT6ndsWPH0KJFC+jp6eHIkSNYuHAhkpOTYWdnh86dO2PatGkFDkpEZdk/4Y/x1d+XkZ4ph5utCVb71Ye1jPd4I6LyRWP2LKkz7lmiskYIgUVH7mD+4VsAeI83IiqbytyeJSIqHakZWfhmx2X8E/7m1kAjm1XDNx2ceesSIiq3GJaISCEuOQ2jNoQi9MFL6GhJMPNjdwxoWPX9MxIRlWEMS0QEALj1NAnD/EPw6GUKTPR1sGyQF5rUeP/VqkREZR3DEhHhxK1nGL/pIpLSMmFvbojVfvVRw7KCqssiIlILDEtE5ZgQAuvO3MfMfdchF0ADRzOsGOSFikZ6qi6NiEhtMCwRlVMZWXLM2HsNG88+BAD09qqCX3rUhp6ORtxfm4io1DAsEZVDCa8zMG7zm1uXSCTAtx2cMbJZtQLda5GIqLxhWCIqZyLjXmH4uhDce/YKhnraWNjPA21deesSIqK8MCwRlSNn7sRhzKaLSEjJgK1MH6v8vOFmy1uXEBHlh2GJqJzYdO4Bpv1zDZlygXp2plg52AuWxrx1CRHR+zAsEZVxmVly/Lz/BvzP3AcAfFzPFnN61YG+Lu9/SERUEAxLRGVYQkoGxm++iFO34wAAX7arhXEta/BEbiKiQmBYIiqj7j1LxqfrLuBe3CsY6GpjXp+66FjbRtVlERFpHIYlojLo1O1nGLfpIhJTM2Er08fKwd5wr8wTuYmIioJhiagMEUJgffADzNx3HVlyAc+qpljuyxO5iYg+BMMSURmRninHtD3XsOX8mxG5e3pWxqyetSHV4YncREQfgmGJqAx4npyGMRsv4vz9FxyRm4iomDEsEWm4608SMWL9BTyOT4GxVAeL+nugpbOlqssiIiozGJaINFjg1Wh8EXAJKRlZcLQwwqrB3qhhWUHVZRERlSkMS0QaSC4XWHjkNhYeuQ0AaFrTAkv6e0JmqKviyoiIyh6GJSINk5yWicnbwnHo2lMAwLAmjviukzN0tLVUXBkRUdnEsESkQR4+f40R6y8g4mkS9LS18EsPd/T2tlN1WUREZRrDEpGGOH0nDuM2X0T86wxYGkux3NcLnlUrqrosIqIyj2GJSM0JIbD6v0j8euAG5AKoa2eKlb5esDLhQJNERKWBYYlIjaVmZOG7nVewM+wxAKCXZxX80sMd+rocaJKIqLQwLBGpqSfxKRi1IRRXHidAW0uC7zu5YGgTBw40SURUyhiWiNTQ+cgXGLspFHHJ6ahoqIs/B3iicQ0LVZdFRFQuMSwRqREhBDacfYCZe68jUy7gYmOClb5esDMzVHVpRETlFsMSkZpIzcjC1N1XsT30EQCgW11bzOlVBwZ6PD+JiEiVGJaI1EB0QgpGbwjFpUcJ0JIAUzq64NOmjjw/iYhIDTAsEalY8N3nGL/5Ip6/SoepoS6W9PfERzV5fhIRkbpgWCJSkezxk2YdvIksuYCrjQlW8PwkIiK1w7BEpAKv0zMxZecV/BP+BADQw6Myfu1Rm+cnERGpIYYlolL24PkrjNoQipsxSdDRkuCHzi7wa8zxk4iI1BXDElEpOnrzKSZuDUdiaiYsKujhzwGeaFjNXNVlERFRPhiWiEqBXC6w8MhtLDxyGwDgWdUUSwd6wVrG+7sREak7hiWiEpbwOgMTAsJwPOIZAGCwjz1+6OwKPR0tFVdGREQFwbBEVIKuPk7AmE2hiHqRAn1dLfzaozZ6elZRdVlERFQIGvNf25cvX8LX1xcymQwymQy+vr6Ij4/Pd54hQ4ZAIpEoPRo1aqTUJi0tDZ999hksLCxgZGSEbt264dGjRyXYEyovAkIeoueyM4h6kYKqZobYOaYJgxIRkQbSmLA0YMAAhIeHIzAwEIGBgQgPD4evr+975+vQoQOio6MVjwMHDii9PnHiROzatQtbt27Ff//9h+TkZHTp0gVZWVkl1RUq41IzsvD135fwzY4rSM+Uo42LJfZ+9hFcbU1UXRoRERWBRhyGu3HjBgIDA3H27Fk0bNgQALBq1Sr4+PggIiICTk5Oec4rlUphbW2d62sJCQlYvXo1NmzYgDZt2gAANm7cCDs7Oxw+fBjt27cv/s5Qmfbw+WuM2RSKa08SoSUBJrdzwpjm1aGlxWEBiIg0lUbsWQoODoZMJlMEJQBo1KgRZDIZzpw5k++8x48fh6WlJWrVqoURI0YgNjZW8VpoaCgyMjLQrl07xTRbW1u4u7u/d7lE7wq6/hSdF5/CtSeJMDPSw/phDTGuZQ0GJSIiDacRe5ZiYmJgaWmZY7qlpSViYmLynK9jx47o3bs37O3tERkZialTp6JVq1YIDQ2FVCpFTEwM9PT0ULFiRaX5rKys8l1uWloa0tLSFM8TExOL0CsqKzKz5Jj7bwRWnLgH4M2wAEsGeMLW1EDFlRERUXFQ6Z6l6dOn5zgB+93HhQsXACDX0Y2FEPmOety3b1907twZ7u7u6Nq1Kw4ePIhbt25h//79+db1vuXOmjVLcaK5TCaDnZ1dAXtMZU1sYioG/HVOEZSGNXHE1pE+DEpERGWISvcsjR8/Hv369cu3jYODAy5fvoynT5/meO3Zs2ewsrIq8PvZ2NjA3t4et2+/GRjQ2toa6enpePnypdLepdjYWDRu3DjP5UyZMgWTJk1SPE9MTGRgKofO3InD51vDEZechgpSHfz2SR10qm2j6rKIiKiYqTQsWVhYwMLC4r3tfHx8kJCQgPPnz6NBgwYAgHPnziEhISHfUPOu58+fIyoqCjY2b37QvLy8oKuri6CgIPTp0wcAEB0djatXr+K3337LczlSqRRSqbTA70tlS5ZcYMnRO1hw5BaEAJytjbF0oCeqVaqg6tKIiKgEaMQJ3i4uLujQoQNGjBiBs2fP4uzZsxgxYgS6dOmidCWcs7Mzdu3aBQBITk7Gl19+ieDgYNy/fx/Hjx9H165dYWFhgR49egAAZDIZhg8fjsmTJ+PIkSMICwvDoEGDULt2bcXVcURvi0tOw5C15zH/8Jug1NfbDrvGNmFQIiIqwzTiBG8A2LRpEz7//HPFlWvdunXDkiVLlNpEREQgISEBAKCtrY0rV65g/fr1iI+Ph42NDVq2bImAgAAYGxsr5pk/fz50dHTQp08fpKSkoHXr1vD394e2tnbpdY40wvnIF/hsy0U8TUyDvq4Wfu5eG594cZBJIqKyTiKEEKouQtMlJiZCJpMhISEBJiYceLCskcsFlh6/g3lBtyAXQPVKRlg60AtO1sbvn5mIiNRWQX+/NWbPEpEqxCWn4YuAcJy6HQcA6OlRGT91d4eRlF8dIqLygn/xifJw9t5zfL4lDLFJbw67zfzYHb29quQ7rAQREZU9DEtE78iSCyw6chuLj96GXAA1LCtg6UBP1LLiYTciovKIYYnoLTEJqZiwNQznIl8AAD7xqoKZH7vBUI9fFSKi8oq/AET/cywiFpO3XcKLV+kw0tPGzz3c0cODV7sREZV3DEtU7qVnyjH30E2sOhUJAHC1McGSAR4cO4mIiAAwLFE5Fxn3Cp9vCcOVx2/G5/LzsceUTi7Q1+U4W0RE9AbDEpVbO0IfYeo/V/E6PQumhrr4rVcdtHOzVnVZRESkZhiWqNxJSs3Aj/9cw66wxwCAho5mWNCvHmxkBiqujIiI1BHDEpUrFx++xIStYYh6kQJtLQkmtq6JsS1rQFuLYycREVHuGJaoXMiSCyw7fgfzD99GllygsqkBFvarB28HM1WXRkREao5hicq8J/EpmBgQjvP/GzupW11b/NzDHSb6uiqujIiINAHDEpVpey49wfe7riApNRNGetr4qbs7enhU5i1LiIiowBiWqExKTM3AtLdO4q5nZ4oFfevBwcJIxZUREZGmYViiMifk/gtM3BqOx/Ep0JIA41vVxGetakBXW0vVpRERkQZiWKIyIz1TjgWHb2H5ibuQC6CqmSHm960HL/uKqi6NiIg0GMMSlQm3niZh4tZwXI9OBPDmBrjTu7mhgpSbOBERfRj+kpBGk8sF1p65jzmBN5GeKUdFQ13M6lkbHdxtVF0aERGVEQxLpLEex6fgq+2XcObucwBAC6dK+K1XHVia6Ku4MiIiKksYlkjjCCHwd+gjzNx7HUlpmTDQ1cb3nV0wsGFVDglARETFjmGJNMqzpDRM2XkFh288BQB4VjXFH33qwZFDAhARUQlhWCKNceBKNH7YfRUvXqVDT1sLX7SthZHNqvG+bkREVKIYlkjtvXyVjqn/XMW+y9EAABcbE8zrUxcuNiYqroyIiMoDhiVSa/9ei8F3u64iLjkN2loSjGtRHeNb1YSeDgeYJCKi0sGwRGop/nU6Zuy9rrhdSU3LCvijT13UqWKq2sKIiKjcYVgitRN4NQY/7H6zN0lLAoxsVh0T29SEvq62qksjIqJyiGGJ1Mbz5DRM23NNcW5S9UpGmNu7Ljyr8nYlRESkOgxLpHJCCOy/Eo1p/1zD81fp0NaSYGSzapjQmnuTiIhI9RiWSKWeJqbih91XEXT9zbhJTlbGmNu7Ds9NIiIitcGwRCohhEBASBR+OXADSamZ0NWWYGyLGhjbsjqkOtybRERE6oNhiUrd/bhX+G7XFcU93epWkWHOJ3XgbM1xk4iISP0wLFGpyciS469TkVhw+BbSMuWQ6mjhy3ZOGPaRI0fhJiIitcWwRKXi8qN4fLPjCm5EJwIAmtQwx689asPenPd0IyIi9cawRCUqOS0T8/69Bf8zkZALwNRQFz90dkUvz8qQSLg3iYiI1B/DEpWYf6/FYNqea4hOSAUAdKtrix+7usKiglTFlRERERUcwxIVuyfxKZi+5xr+/d9wAHZmBvi5e200r1VJxZUREREVHsMSFZuMLDn8T9/H/MO38Do9Czr/G1zys1Y1YaDH4QCIiEgzMSxRsbhw/wV+2H0VN2OSAADe9hXxS4/acLI2VnFlREREH4ZhiT7Ii1fpmH3wBrZdeAQAqGioiykdXfCJVxVocTgAIiIqA7RUXUBBvXz5Er6+vpDJZJDJZPD19UV8fHy+80gkklwfc+fOVbRp0aJFjtf79etXwr3RfFlygY1nH6Dl78cVQalffTscndwCferbMSgREVGZoTF7lgYMGIBHjx4hMDAQADBy5Ej4+vpi7969ec4THR2t9PzgwYMYPnw4evXqpTR9xIgRmDlzpuK5gYFBMVZe9oQ9fImp/1zF1cdvxkxytjbGLz3c4WVvpuLKiIiIip9GhKUbN24gMDAQZ8+eRcOGDQEAq1atgo+PDyIiIuDk5JTrfNbW1krP//nnH7Rs2RLVqlVTmm5oaJijLeUUl5yGuYERCLgQBQAw1tfBl+2cMLBhVehoa8xOSiIiokLRiF+44OBgyGQyRVACgEaNGkEmk+HMmTMFWsbTp0+xf/9+DB8+PMdrmzZtgoWFBdzc3PDll18iKSmp2GovCzKy5Fj9XyRa/n5cEZQ+8aqCo5NbwK+xA4MSERGVaRqxZykmJgaWlpY5pltaWiImJqZAy1i3bh2MjY3Rs2dPpekDBw6Eo6MjrK2tcfXqVUyZMgWXLl1CUFBQnstKS0tDWlqa4nliYmIBe6J5Tt1+hhl7r+NObDIAoHZlGaZ3c+UhNyIiKjdUGpamT5+OGTNm5NsmJCQEAHK9NYYQosC3zFizZg0GDhwIfX19pekjRoxQ/Nvd3R01a9aEt7c3Ll68CE9Pz1yXNWvWrPfWreki417h1wM3EPS/gSXNjfTwVXsn9Pa2401viYioXFFpWBo/fvx7rzxzcHDA5cuX8fTp0xyvPXv2DFZWVu99n1OnTiEiIgIBAQHvbevp6QldXV3cvn07z7A0ZcoUTJo0SfE8MTERdnZ27122JkhMzcCSo3ew9nQkMrIEtLUk8PNxwIQ2NSEz0FV1eURERKVOpWHJwsICFhYW723n4+ODhIQEnD9/Hg0aNAAAnDt3DgkJCWjcuPF751+9ejW8vLxQt27d97a9du0aMjIyYGNjk2cbqVQKqbRs3d8sM0uOgAtRmPfvLTx/lQ4AaF6rEqZ2cUENSw4sSURE5ZdECCFUXURBdOzYEU+ePMGKFSsAvBk6wN7eXmnoAGdnZ8yaNQs9evRQTEtMTISNjQ3++OMPjB49WmmZd+/exaZNm9CpUydYWFjg+vXrmDx5MgwMDBASEgJt7YLdoiMxMREymQwJCQkwMTEpht6WruMRsfj1wA3cevrmvKTqlYzwQxdXtHTKeZ4YERFRWVHQ32+NOMEbeHPF2ueff4527doBALp164YlS5YotYmIiEBCQoLStK1bt0IIgf79++dYpp6eHo4cOYKFCxciOTkZdnZ26Ny5M6ZNm1bgoKTJbsYk4pf9N3DqdhwAQGagiwmta8LXxx66vMKNiIgIgAbtWVJnmrZn6WliKuYH3cK2C1GQC0BX+815SZ+1qgmZIc9LIiKi8qHM7VmiD5eYmoEVJ+5i9X+RSM2QAwA61bbGNx2cYW9upOLqiIiI1BPDUjmQlpmFzeceYtGR23j5OgMA4G1fEVM6OXO8JCIiovdgWCrDsuQCu8MeY/7hW3j0MgUAUK2SEb7t4Iy2rlYFHqOKiIioPGNYKoOEEAi6/hS//xuhuMLN0liKCW1qoq+3HW9PQkREVAgMS2WIEAKn7zzH7/9GIDwqHgBgoq+DsS1rwM/HAQZ6Zf8KPyIiouLGsFRGhNx/gd8PReBc5AsAgIGuNoY2ccCoZtV5hRsREdEHYFjScOFR8ZgfdAsnbj0DAOhpa2FAw6oY27I6LI313zM3ERERvQ/DkoYKj4rHwsO3cCziTUjS0ZKgt7cdPmtVA7amBiqujoiIqOxgWNIw74YkbS0JenhUxmetanCsJCIiohLAsKQhzke+wOKjtxW3JskOSeNb1oCDBUMSERFRSWFYUmPZV7ctPnpbceK2tpYE3eu92ZPEkERERFTyGJbU2NhNF3HwagyAN/dv6+1thzHNq8POzFDFlREREZUfDEtqrL6DGY7ejEX/BlUxqnk12Mh44jYREVFpY1hSYwMaVkXXuraoZCxVdSlERETlFsOSGtPX1Ya+LkfdJiIiUiXeJIyIiIgoHwxLRERERPlgWCIiIiLKB8MSERERUT4YloiIiIjywbBERERElA+GJSIiIqJ8MCwRERER5YNhiYiIiCgfDEtERERE+WBYIiIiIsoHwxIRERFRPhiWiIiIiPKho+oCygIhBAAgMTFRxZUQERFRQWX/bmf/jueFYakYJCUlAQDs7OxUXAkREREVVlJSEmQyWZ6vS8T74hS9l1wux5MnT2BsbAyJRFJsy01MTISdnR2ioqJgYmJSbMtVJ2W9j2W9f0DZ7yP7p/nKeh/Zv6ITQiApKQm2trbQ0sr7zCTuWSoGWlpaqFKlSokt38TEpEx+Ad5W1vtY1vsHlP0+sn+ar6z3kf0rmvz2KGXjCd5ERERE+WBYIiIiIsoHw5Iak0qlmDZtGqRSqapLKTFlvY9lvX9A2e8j+6f5ynof2b+SxxO8iYiIiPLBPUtERERE+WBYIiIiIsoHwxIRERFRPhiWiIiIiPLBsKRiv/zyCxo3bgxDQ0OYmpoWaB4hBKZPnw5bW1sYGBigRYsWuHbtmlKbtLQ0fPbZZ7CwsICRkRG6deuGR48elUAP8vfy5Uv4+vpCJpNBJpPB19cX8fHx+c4jkUhyfcydO1fRpkWLFjle79evXwn3Jqei9G/IkCE5am/UqJFSG3VZf0Dh+5iRkYFvvvkGtWvXhpGREWxtbTF48GA8efJEqZ2q1uHSpUvh6OgIfX19eHl54dSpU/m2P3HiBLy8vKCvr49q1aph+fLlOdrs2LEDrq6ukEqlcHV1xa5du0qq/AIpTB937tyJtm3bolKlSjAxMYGPjw8OHTqk1Mbf3z/X72RqampJdyVXhenf8ePHc6395s2bSu3UaR0Wpn+5/T2RSCRwc3NTtFGn9Xfy5El07doVtra2kEgk2L1793vnUYvvoCCV+vHHH8W8efPEpEmThEwmK9A8s2fPFsbGxmLHjh3iypUrom/fvsLGxkYkJiYq2owePVpUrlxZBAUFiYsXL4qWLVuKunXriszMzBLqSe46dOgg3N3dxZkzZ8SZM2eEu7u76NKlS77zREdHKz3WrFkjJBKJuHv3rqJN8+bNxYgRI5TaxcfHl3R3cihK//z8/ESHDh2Uan/+/LlSG3VZf0IUvo/x8fGiTZs2IiAgQNy8eVMEBweLhg0bCi8vL6V2qliHW7duFbq6umLVqlXi+vXrYsKECcLIyEg8ePAg1/b37t0ThoaGYsKECeL69eti1apVQldXV/z999+KNmfOnBHa2tri119/FTdu3BC//vqr0NHREWfPni3RvuSlsH2cMGGCmDNnjjh//ry4deuWmDJlitDV1RUXL15UtFm7dq0wMTHJ8d1UhcL279ixYwKAiIiIUKr97e+SOq3DwvYvPj5eqV9RUVHCzMxMTJs2TdFGndbfgQMHxPfffy927NghAIhdu3bl215dvoMMS2pi7dq1BQpLcrlcWFtbi9mzZyumpaamCplMJpYvXy6EePPl0dXVFVu3blW0efz4sdDS0hKBgYHFXnterl+/LgAobbDBwcECgLh582aBl/Pxxx+LVq1aKU1r3ry5mDBhQnGVWiRF7Z+fn5/4+OOP83xdXdafEMW3Ds+fPy8AKP3BV8U6bNCggRg9erTSNGdnZ/Htt9/m2v7rr78Wzs7OStNGjRolGjVqpHjep08f0aFDB6U27du3F/369SumqgunsH3Mjaurq5gxY4bieUH/PpWGwvYvOyy9fPkyz2Wq0zr80PW3a9cuIZFIxP379xXT1Gn9va0gYUldvoM8DKdhIiMjERMTg3bt2immSaVSNG/eHGfOnAEAhIaGIiMjQ6mNra0t3N3dFW1KQ3BwMGQyGRo2bKiY1qhRI8hksgLX8fTpU+zfvx/Dhw/P8dqmTZtgYWEBNzc3fPnll0hKSiq22gviQ/p3/PhxWFpaolatWhgxYgRiY2MVr6nL+gOKZx0CQEJCAiQSSY5DzaW5DtPT0xEaGqr0uQJAu3bt8uxLcHBwjvbt27fHhQsXkJGRkW+b0l5XQNH6+C65XI6kpCSYmZkpTU9OToa9vT2qVKmCLl26ICwsrNjqLqgP6Z+HhwdsbGzQunVrHDt2TOk1dVmHxbH+Vq9ejTZt2sDe3l5pujqsv6JQl+8gb6SrYWJiYgAAVlZWStOtrKzw4MEDRRs9PT1UrFgxR5vs+UtDTEwMLC0tc0y3tLQscB3r1q2DsbExevbsqTR94MCBcHR0hLW1Na5evYopU6bg0qVLCAoKKpbaC6Ko/evYsSN69+4Ne3t7REZGYurUqWjVqhVCQ0MhlUrVZv0BxbMOU1NT8e2332LAgAFKN8Es7XUYFxeHrKysXL87efUlJiYm1/aZmZmIi4uDjY1Nnm1Ke10BRevju/744w+8evUKffr0UUxzdnaGv78/ateujcTERCxcuBBNmjTBpUuXULNmzWLtQ36K0j8bGxusXLkSXl5eSEtLw4YNG9C6dWscP34czZo1A5D3ei7tdfih6y86OhoHDx7E5s2blaary/orCnX5DjIslYDp06djxowZ+bYJCQmBt7d3kd9DIpEoPRdC5Jj2roK0KYiC9g/IWWdh61izZg0GDhwIfX19pekjRoxQ/Nvd3R01a9aEt7c3Ll68CE9PzwItOy8l3b++ffsq/u3u7g5vb2/Y29tj//79OUJhYZZbGKW1DjMyMtCvXz/I5XIsXbpU6bWSXIf5Kex3J7f2704vyvexJBW1ni1btmD69On4559/lEJyo0aNlC5CaNKkCTw9PbF48WIsWrSo+AovoML0z8nJCU5OTornPj4+iIqKwu+//64IS4VdZkkrai3+/v4wNTVF9+7dlaar2/orLHX4DjIslYDx48e/96oeBweHIi3b2toawJu0bWNjo5geGxurSNbW1tZIT0/Hy5cvlfZOxMbGonHjxkV637cVtH+XL1/G06dPc7z27NmzHP8LyM2pU6cQERGBgICA97b19PSErq4ubt++/cE/tKXVv2w2Njawt7fH7du3AZT8+gNKp48ZGRno06cPIiMjcfToUaW9SrkpznWYGwsLC2hra+f43+bb3513WVtb59peR0cH5ubm+bYpzDZQXIrSx2wBAQEYPnw4tm/fjjZt2uTbVktLC/Xr11dss6XlQ/r3tkaNGmHjxo2K5+qyDj+kf0IIrFmzBr6+vtDT08u3rarWX1GozXew2M5+og9S2BO858yZo5iWlpaW6wneAQEBijZPnjxR2Qne586dU0w7e/ZsgU8O9vPzy3EFVV6uXLkiAIgTJ04Uud7C+tD+ZYuLixNSqVSsW7dOCKE+60+IovcxPT1ddO/eXbi5uYnY2NgCvVdprMMGDRqIMWPGKE1zcXHJ9wRvFxcXpWmjR4/OcXJpx44dldp06NBBpSd4F6aPQgixefNmoa+v/96TbbPJ5XLh7e0thg4d+iGlFklR+veuXr16iZYtWyqeq9M6LGr/sk9kv3LlynvfQ5Xr720o4Ane6vAdZFhSsQcPHoiwsDAxY8YMUaFCBREWFibCwsJEUlKSoo2Tk5PYuXOn4vns2bOFTCYTO3fuFFeuXBH9+/fPdeiAKlWqiMOHD4uLFy+KVq1aqWzogDp16ojg4GARHBwsateuneOy83f7J4QQCQkJwtDQUCxbtizHMu/cuSNmzJghQkJCRGRkpNi/f79wdnYWHh4eat+/pKQkMXnyZHHmzBkRGRkpjh07Jnx8fETlypXVcv0JUfg+ZmRkiG7duokqVaqI8PBwpUuV09LShBCqW4fZl2WvXr1aXL9+XUycOFEYGRkprhz69ttvha+vr6J99mXLX3zxhbh+/bpYvXp1jsuWT58+LbS1tcXs2bPFjRs3xOzZs9Vi6ICC9nHz5s1CR0dH/Pnnn3kO4zB9+nQRGBgo7t69K8LCwsTQoUOFjo6OUohW1/7Nnz9f7Nq1S9y6dUtcvXpVfPvttwKA2LFjh6KNOq3DwvYv26BBg0TDhg1zXaY6rb+kpCTF7xwAMW/ePBEWFqa4UlZdv4MMSyrm5+cnAOR4HDt2TNEGgFi7dq3iuVwuF9OmTRPW1tZCKpWKZs2a5fjfREpKihg/frwwMzMTBgYGokuXLuLhw4el1Kv/9/z5czFw4EBhbGwsjI2NxcCBA3Ncwvtu/4QQYsWKFcLAwCDXcXcePnwomjVrJszMzISenp6oXr26+Pzzz3OMVVQaCtu/169fi3bt2olKlSoJXV1dUbVqVeHn55dj3ajL+hOi8H2MjIzMdZt+e7tW5Tr8888/hb29vdDT0xOenp5Ke7L8/PxE8+bNldofP35ceHh4CD09PeHg4JBrgN++fbtwcnISurq6wtnZWemHWBUK08fmzZvnuq78/PwUbSZOnCiqVq0q9PT0RKVKlUS7du3EmTNnSrFHygrTvzlz5ojq1asLfX19UbFiRfHRRx+J/fv351imOq3Dwm6j8fHxwsDAQKxcuTLX5anT+sveA5bX9qau30GJEP87U4qIiIiIcuA4S0RERET5YFgiIiIiygfDEhEREVE+GJaIiIiI8sGwRERERJQPhiUiIiKifDAsEREREeWDYYmIiIgoHwxLRERERPlgWCIiIiLKB8MSEdE7nj17Bmtra/z666+KaefOnYOenh7+/fdfFVZGRKrAe8MREeXiwIED6N69O86cOQNnZ2d4eHigc+fOWLBggapLI6JSxrBERJSHcePG4fDhw6hfvz4uXbqEkJAQ6Ovrq7osIiplDEtERHlISUmBu7s7oqKicOHCBdSpU0fVJRGRCvCcJSKiPNy7dw9PnjyBXC7HgwcPVF0OEakI9ywREeUiPT0dDRo0QL169eDs7Ix58+bhypUrsLKyUnVpRFTKGJaIiHLx1Vdf4e+//8alS5dQoUIFtGzZEsbGxti3b5+qSyOiUsbDcERE7zh+/DgWLFiADRs2wMTEBFpaWtiwYQP+++8/LFu2TNXlEVEp454lIiIionxwzxIRERFRPhiWiIiIiPLBsERERESUD4YlIiIionwwLBERERHlg2GJiIiIKB8MS0RERET5YFgiIiIiygfDEhEREVE+GJaIiIiI8sGwRERERJQPhiUiIiKifPwfB3gW76EemAYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.polynomial.chebyshev import chebfit, chebval\n",
    "\n",
    "# 定义要逼近的函数\n",
    "def f(x):\n",
    "    return np.sin(x)\n",
    "\n",
    "# 生成 x 值范围\n",
    "x = np.linspace(-1, 1, 100)\n",
    "\n",
    "# 使用切比雪夫多项式逼近\n",
    "degree = 40  # 选择逼近的多项式的阶数\n",
    "cheb_coeffs = chebfit(x, f(x), degree)\n",
    "print(chebfit)\n",
    "\n",
    "# 使用得到的切比雪夫系数计算逼近值\n",
    "f_approx = chebval(x, cheb_coeffs)\n",
    "\n",
    "# 绘图对比原始函数和逼近结果\n",
    "plt.plot(x, f(x), label='Original Function')\n",
    "plt.plot(x, f_approx, label=f'Chebyshev Approximation (degree={degree})')\n",
    "plt.legend()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.title('Chebyshev Polynomial Approximation of sin(x)')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b15742fa-7ea9-4cca-9858-5402fd9deda3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
